Free Mixed Air Temperature Calculator

混合空气温度计算器简介

The mixed air temperature calculator is an online tool that determines the final temperature when two gas streams at distinct temperatures and mix ratios are combined. It can be employed as an HVAC mixed air temperature calculator for computing the supply air temperature in heating, ventilation, and air conditioning systems, as a gas mixing temperature calculator for industrial and laboratory applications, and as a supply air temperature calculator for HVAC engineering. Because the mix temperature represents the thermal equilibrium temperature of the combined stream, the calculator is also commonly referred to as an air mixing calculator. The calculation uses a weighted-average formula, which is straightforward yet widely applicable.

混合温度公式

The fundamental equation for two-component mixing is a weighted average of the individual temperatures. Using mass, volume, or mole fractions as weights ($w_1$ and $w_2$), the mixed temperature is given by:

$$T_{\text{mix}} = \frac{T_1 \, w_1 + T_2 \, w_2}{w_1 + w_2}$$

If the proportions are expressed as percentages ($P_1$ and $P_2$) that sum to 100%, the equation simplifies to:

$$T_{\text{mix}} = \frac{T_1 P_1 + T_2 P_2}{100}$$

Since both gases occupy the entire reservoir, $P_1 + P_2 = 100\%$ (or $w_1 + w_2 = 1$ when using fractional weights). The formula assumes no phase change, constant specific heats, and complete thermal equilibrium after mixing. From an energy balance perspective, if both streams have the same specific heat capacity, the weighted average naturally emerges:

$$m_1 c_p (T_1 - T_{\text{mix}}) = m_2 c_p (T_{\text{mix}} - T_2) \quad\Longrightarrow\quad T_{\text{mix}} = \frac{m_1 T_1 + m_2 T_2}{m_1 + m_2}$$

where $m_1$ and $m_2$ are the masses of the two portions.

The following table shows how the mixing temperature changes with different percentage splits for a fixed pair of temperatures (10°C and 30°C):

P1 (%)	P2 (%)	Tmix (°C)
0	100	30.0
20	80	26.0
40	60	22.0
50	50	20.0
60	40	18.0
80	20	14.0
100	0	10.0

As the table illustrates, the result is linearly dependent on the proportions, making the formula easy to use in practice.

HVAC 供气温度计算

In HVAC systems, the supply air is a mixture of outdoor air and recirculated return air. The supply air temperature is a critical parameter for system sizing and indoor comfort. The formula adapted for HVAC uses volumetric flow rates (in cubic feet per minute, CFM) as weights:

$$T_s = \frac{T_{\text{oa}} \cdot \text{CFM}_{\text{oa}} + T_{\text{ra}} \cdot \text{CFM}_{\text{ra}}}{\text{CFM}_{\text{oa}} + \text{CFM}_{\text{ra}}}$$

Variables:

• $T_{\text{oa}}$ – outdoor air temperature (°C or °F)
• $\text{CFM}_{\text{oa}}$ – outdoor airflow rate (CFM)
• $T_{\text{ra}}$ – return air temperature
• $\text{CFM}_{\text{ra}}$ – return airflow rate
• $T_s$ – supply air temperature (the result)

计算实例

Consider a house requiring 1,400 CFM total supply. Outdoor air enters at 30°C with a flow of 60 CFM; the remaining 1,340 CFM is return air at 23°C. Applying the formula:

$$T_s = \frac{30 \times 60 + 23 \times 1340}{60 + 1340} = \frac{1800 + 30820}{1400} = \frac{32620}{1400} \approx 23.3^\circ\text{C}$$

Thus, the supply air temperature delivered to the conditioned space is about 23.3°C, illustrating the moderating effect of mixing warm outdoor air with cooler indoor return air. The supply temperature is much closer to the return temperature because the return flow dominates. The table below shows how varying the outdoor air flow (while keeping total flow fixed) changes the result:

Outdoor Air (CFM)	Return Air (CFM)	Ts (°C)
0	1400	23.0
60	1340	23.3
200	1200	24.0
500	900	25.5
1400	0	30.0

This demonstrates that increasing the outdoor air fraction raises the supply temperature, which affects cooling coil load and energy consumption.

气体温度的基本概念

Temperature is a measure of the average kinetic energy of gas molecules; faster molecular motion corresponds to a higher temperature. In practice, gas temperature is measured using sensors such as thermocouples, resistance temperature detectors (RTDs), and thermistors. For an ideal gas, temperature can also be derived from the ideal gas law:

$$PV = nRT$$

where $P$ is pressure (Pa), $V$ is volume (m³), $n$ is number of moles, $R = 8.31446 \; \text{J/(K·mol)}$ is the universal gas constant, and $T$ is the absolute temperature in Kelvin. This relation is often used in scientific calculations, though it applies accurately only to ideal or near-ideal gases. For real gases, corrections such as the van der Waals equation may be needed, but the ideal gas law remains a good approximation at low pressures and moderate temperatures.

热平衡与热力学基础

Thermal equilibrium describes a state where two or more systems share the same temperature and no net heat transfer occurs between them. The Zeroth Law of Thermodynamics establishes the foundation for temperature measurement: if system A is in equilibrium with system B, and system B with system C, then A and C are also in thermal equilibrium. Consequently, temperature can be defined consistently across different objects. Whenever a temperature gradient exists, heat flows spontaneously from the hotter to the colder system until equilibrium is reached. The mixed air temperature calculator directly applies this principle—when two gases mix, heat is exchanged until a uniform temperature is achieved.

温标与实际换算

Temperature can be expressed using different scales. The most common are the Celsius scale (°C) and the Kelvin scale (K). On the Celsius scale, water freezes at 0°C and boils at 100°C under standard atmospheric pressure. The Kelvin scale starts at absolute zero (0 K), the lowest theoretically achievable temperature, and uses the same increment size as the Celsius scale. The conversion between them is:

$$T(\text{K}) = T(^\circ\text{C}) + 273.15$$

While the mixed air temperature formula itself is independent of the chosen scale, consistent unit usage is essential. When applying the ideal gas law, temperature must be in Kelvin. Many online calculators, including this one, allow users to input temperatures in °C, °F, or K and perform necessary conversions automatically.

典型应用场景

The mixed air temperature calculator finds use in several fields:

• HVAC engineering: sizing air handling units, determining coil loads, and optimizing energy recovery. For example, in an economizer mode, the calculator helps decide how much outdoor air to introduce to achieve a target supply temperature while minimizing mechanical cooling.
• Gas mixing in industry: predicting the temperature of blended gases (e.g., natural gas and air) for combustion or process control. The same weighted average applies whether the gases are air, nitrogen, oxygen, or other common gases.
• Laboratory work: preparing gas mixtures with specific thermal characteristics, such as calibration gases for analyzers.
• Environmental analysis: evaluating dilution of hot exhaust gases with ambient air to estimate stack exit temperatures or plume rise.

重要使用说明

To obtain correct results, keep the following points in mind:

• The sum of the two component proportions must equal 100% (or 1); otherwise the output is meaningless.
• For HVAC calculations, ensure flow rates are in the same unit (e.g., CFM). If using other units (m³/h, L/s), convert them before entering.
• The weighted-average formula assumes constant specific heats, no condensation or phase change, and complete mixing with negligible heat loss to surroundings. These assumptions hold well for typical HVAC and many gas-blending scenarios.
• The calculator can also solve for an unknown input (e.g., required outdoor air temperature or flow to achieve a target supply temperature) via algebraic rearrangement of the same equation. For instance, if $T_s$ is specified, the required outdoor air flow can be expressed as $\text{CFM}_{\text{oa}} = \text{CFM}_{\text{total}} \cdot \frac{T_s - T_{\text{ra}}}{T_{\text{oa}} - T_{\text{ra}}}$, assuming $T_{\text{oa}} \neq T_{\text{ra}}$.